The study that we present is part of a broader research project on the possibilities of improving critical literacy in the face of the media and social networks of communication, in the initial training of secondary education teachers, in line with the efforts that UNESCO has been developing through the collaboration of an international network of universities. The main objective of the specific case that we present is to know the attitudes and communicative behaviour of students in the Master's Degree in Teaching Program in the face of hate speech and violence, in the context of multimodal media, as well as the perception they have about their own competence to train future students in media literacy and the importance they attach to it. As an instrument to achieve this goal, a questionnaire was chosen to describe the conditions of the media reality that students appreciate, identify norms and patterns of these conditions and actions, and determine relationships between these and their opinions regarding the education of their future students on the subject. A sample of students from the University of Cadiz responded (n = 72), stating conclusive positions regarding the importance of literacy or media literacy, but contrary to expectations, they do not have a homogeneous media culture. On the other hand, they do coincide in a perspective of the experience of interaction focused on the personal and pay little attention to disruptive phenomena in the media and digital networks. Therefore, when they have an incident with aggressive speech, it affects them drastically, and they have no strategies to deal with it. However, they perceive themselves prepared to educate their future students on the subject. We believe that these results justify the need to implement specific training in critical media literacy for future secondary school teachers.